Cortical cell assemblies and their underlying connectivity: An in silico study

Recent developments in experimental techniques have enabled simultaneous recordings from thousands of neurons, enabling the study of functional cell assemblies. However, determining the patterns of synaptic connectivity giving rise to these assemblies remains challenging. To address this, we developed a complementary, simulation-based approach, using a detailed, large-scale cortical network model. Using a combination of established methods we detected functional cell assemblies from the stimulus-evoked spiking activity of 186,665 neurons. We studied how the structure of synaptic connectivity underlies assembly composition, quantifying the effects of thalamic innervation, recurrent connectivity, and the spatial arrangement of synapses on dendrites. We determined that these features reduce up to 30%, 22%, and 10% of the uncertainty of a neuron belonging to an assembly. The detected assemblies were activated in a stimulus-specific sequence and were grouped based on their position in the sequence. We found that the different groups were affected to different degrees by the structural features we considered. Additionally, connectivity was more predictive of assembly membership if its direction aligned with the temporal order of assembly activation, if it originated from strongly interconnected populations, and if synapses clustered on dendritic branches. In summary, reversing Hebb’s postulate, we showed how cells that are wired together, fire together, quantifying how connectivity patterns interact to shape the emergence of assemblies. This includes a qualitative aspect of connectivity: not just the amount, but also the local structure matters; from the subcellular level in the form of dendritic clustering to the presence of specific network motifs.

First and foremost, the work focuses exclusively on assemblies directly evoked by injected stimuli, with no mentions of spontaneous activity.However a lot of interest is devoted to why and by which mechanisms assemblies emerge during spontaneous activity, and on the similarities between the spontaneous assemblies and those evoked by stimuli (e.g. refs [10,11,13,58] in main text).I think it should be explained why this aspect has not been investigated in the paper, despite its centrality in both experimental and modeling work.

Response:
We understand the importance of spontaneous assemblies and their link to evoked assemblies in the field and that we failed to acknowledge them in the previous version.We now explicitly mention spontaneous assemblies and work related to them in the introduction (lines 39-41; 70-72) and motivate our decision to focus on evoked assemblies (lines 73-74).
Briefly, while we believe that our model is a suitable tool to study also spontaneous assemblies, it would require either the re-calibration of the spontaneous state (see Isbister et al., 2023, bioRxiv) for higher amplitude fluctuations in the total activity yielding a subset of the time bins to cluster.Without recalibration, spontaneous activity has low fluctuations in the total activity, i.e., nearly all time bins are significant.Thus, we would need to extend the current assembly detection methods in order to handle the large number of time bins and neurons present in our simulations; which is computationally expensive.We therefore believe that this is outside the scope of this work.Second, I find it curious that about 150 ms after stimulus onset the same, broadly distributed late assembly activates for every stimulus in the input set.This is an interesting model prediction I am not fully convinced about (it seems unjustified in terms of energy cost, for a patterns that seems quite uninformative).I also wonder how much of it is due to the presence of the broad, unspecific POm component that comes with every input stimulus.For example it would be interesting to see if it is still present in the absence of POm stimulus, and to what extent.Perhaps it should be better explained and justified why input stimuli have both a clustered and a more spread-out component.

Response:
We agree that such a non-specific assembly is unlikely to exist in vivo.We repeated the simulation campaign without the POm stimulus and found that this does not make the late assembly stimulus-specific (added as Supplementary Figure S9).
We now present two hypotheses to explain the emergence of this phenomenon in the model in lines 452-463.A stimulus-specific late assembly may emerge through plasticity, or require interaction with other brain regions through feed-back connections and not be a phenomenon of the local circuitry alone.The second hypothesis is supported by the lower firing rate of the late assembly, as outlined in the text and in Supplementary Figure S1C.P17 , POm stimulus.I suggest to mention this in the results section as well.Also, it is not clear whether the POm fibers were randomly sampled only once for each VPM pattern and associated to it as frozen noise, or resampled independently at each stimulus presentation.The result section simply states "The stream consisted of repeated presentations of 10 different input patterns in random order", suggesting that they are sampled only once.

Response:
We made the frozen, non-stimulus specific nature of the POm part of the stimuli clearer in both the Results and Methods sections (lines 103-104 and 560; 563).

Reviewer #2:
Assemblies of neurons firing together in the isocortex have been studied using in vivo recording methods, and their activity has been linked to different aspects of cortical coding.However, these in vivo methods lack information about structural connectivity, cell type identity, and subcellular synaptic specificity.This study uses a preexisting large, biophysically detailed model of rat somatosensory cortex to investigate the structural contributions to the formations of coactive neuronal assemblies.The authors quantify the effects of thalamic innervation, recurrent connectivity, subcellular targeting in determining membership of cell assemblies that occur at different times after stimulus presentation to the model.They find that the factors can be predictive, although the degree of contribution changes based on the time of assembly activity.
Overall, the study is quite interesting, well-designed, and generally well-presented.The use of a model where connectivity and neuronal identities are entirely known is a powerful approach to testing the influence of structural factors.This approach could also generate predictions for future in vivo experiments (especially those that are combined with post hoc connectivity measurements, like large-volume electron microscopy reconstruction).I only have a few suggestions to potentially improve the clarity of the manuscript or add information of interest to the community.

Response: We thank the reviewer for the kind summary of our work.
There are a few places where I felt there was a slight disconnect between the text and the figures.In the last paragraph of page 8, the authors discuss the notion of "k-indegree with respect to an assembly", and discuss results for 0-indegree before moving to 1-, 2-, and 3-indegree.The results for 0-indegree are presented in Figure 4D, but there is no specific mention of "0-indegree" (the authors just use the term "indegree" without a modifier), so it was unclear to me at first which results were specific to the 0-indegree analysis.I think it would be clearer if the "0-indegree" term was explicitly used in Fig. 4D.After this text, the authors then go on to say they will refer to 0-indegree as just "indegree" in later figures, but I think in Figure 4 it would better align with the text if "0-indegree" was explicitly used.

Response:
We addressed this together with a similar concern voiced by Reviewer #1 (we repeat that response here for easy finding).We updated the axis labels on Figure 4, moved the mentioning of 0-indegree being equivalent to indegree to the beginning of section 2.2.2 and kept using 0-indegree consistently afterwards.
Also, for the results shown in Figure 6, the authors define a measure of "coreness" (discussed in the results and methods), but it seems as though this measure is not directly presented in Figure 6. Figure 6B has neurons grouped by "fraction of assemblies" instead, which seems to be similar to the "coreness" metric but not exactly the same.I think it would be clearer if a consistent measure were discussed and presented (or at least describe the differences between the measures).

Response:
We originally depicted in Figure 6 a measure that was related to, but slightly different from "coreness" as defined.We understand that this was needlessly confusing for the reader.We have updated Figure 6 to use coreness instead.
Lastly, since cellular identity (as well as connectivity) is completely known in the model, I was curious if there were any cell-type specific results for assemblies or for the effect of innervating k-cliques.For example, are there k-cliques comprising particular combinations of cell types (types of inhibitory vs excitatory; types of excitatory cells within/across layers, etc.) that are more likely to lead to a cell joining an assembly than others?There is a fair amount of discussion of the layers in which the neurons belonging to different assemblies reside, but I think some additional analysis of cell type could be of great interest to readers interested in assigning circuit roles to particular types.

Response: We appreciate the importance of understanding the roles of different classes of neurons and their interactions. However, in the context of an analysis of directed simplices, this becomes very challenging. The model contains 18 excitatory neuron types, each of them could be studied with respect to their roles as innervating or innervated neurons. Additionally, the effect can be considered for different simplex dimensions, and for different assemblies (most effects played out very differently for early, middle and late assemblies). This leads to a combinatorial explosion of different cases with many, possibly inter-dependent effects.
To illustrate this, we considered the question of how 3-indegree from the late assembly affects morphological types (m-types) differently, see Figure R1 in this document.Indeed, we can see that neurons of the L6 TPC:A,C and L5 TPC:A,B,C types were less affected in late assembly membership by having a low 3-indegree than other types.However, this leads to knock-on questions: Is this a property specific to the late assembly?Is this a property of these types to be less affected by connectivity, or are there correlations with the other factors studied?(Such as thalamic inputs; also clustering could have a stronger effect due to larger dendrite sizes of thick-tufted classes).This further enhances the combinatorial explosion of things to study.
That is why the additional dimension of neuron types is best studied not in an exploratory fashion, but with a specific hypothesis in mind.We believe this is out of scope for the present manuscript.We note that an interested reader could conduct analyses of the impact of neuron types using the data we made available.

Figure R1: Effect of mtype on assembly membership filtered by 3-indegree. A: Global effect of 3-indegree from the late assembly in facilitating membership in the late assembly. Low (L) and High (H) 3-indegree from the late assembly represent 25% of the neurons with lowest and highest 3-indegree values respectively, the 50% remaining is classified as Medium (M) 3-indegree. B: Effect of mtype in assembly membership once the global effect depicted in panel A is normalized out. Left to right: three categories of Low (L), Medium (M) and High (H) 3-indegree from the late assembly. Each panel shows the probability that a neuron is of a given mtype, given that it has L/M/H 3-indegree and belongs or not to an assembly, normalized by the probability that a neuron is of that given mtype given that it has L/M/H 3-indegree irrespective of assembly membership. Values higher/lower than 1 show over/under expression of the neurons of that class.
Overall, this is a strong and interesting study making good use of a large-scale, biophysically detailed model that should enable future directions of research.

Response:
We once again thank the reviewer for the kind words.

Reviewer 3:
This manuscript studied a very interesting topic: how are neural assemblies formed by simulating a large-scale in silico model.The in silico study can provide many insights that cannot be discovered in current wet experiments.The study is comprehensive and timely.However, the comprehensive methods also bring up many questions for me, see blow.

Response:
We thank the reviewer for the positive words. Major: -Can this study provide any experimentally testable prediction under current experimental methodology?
Response: Yes, we believe that many of our predictions are testable, but we neglected to write about that in the discussion.We have added lines 443-449 to the discussion, where we outline our attempt to test our predictions in the MICrONS dataset, why it was not possible, and why we believe that it will be possible in the near future using additional EM datasets with co-registered activity data.
-The study used so many "arbitrary" values to characterize the assembly.This begs the question if the conclusion depends on those choices?For example, --although the authors cited Harris et al to validate the choice of 20 ms time bins, I am still curious would the conclusion change if this bin length changes.

Response:
We agree that demonstrating robustness of our methods with respect to parameter choices is important.We have therefore repeated our analyses with smaller and larger time bins and compared the results to the originally chosen time bins.We describe the results of this comparison in lines 412-419 and Supplementary Figure S7.
--How did the authors justify the amplitude of inputs?
Response: "We now outline the calibration of stimulus amplitudes in lines 556-560." -In main text/figure caption, it would be much better to intuitively and shortly explain the physical meaning (not only definition but what it can do) of many concepts and terms, such as input/output distance, clustering of significant time bins, k-simplices

Response:
We now provide a more intuitive explanation of the measure of normalized information (nI) in lines 197-206.We now provide short explanations of how to interpret the input and output distances in the caption of Figure 3.We provide an explanation of what the clustering method optimizes (minimization of total within-cluster variance) in lines 580-581.We explain k-simplices in the caption of Figure 4, where we first use them.
-"We found that assemblies were activated in all stimulus repetitions and a series of two to three assemblies remained active for 110 \pm 30 ms".It would be even nicer to show distribution of the assembly lifetime.Is it possible that the assembly is like the neural avalanche?

Response:
The relation of our work to the neural avalanches is indeed an interesting question.We explored the duration of assembly sequences and activated neuron counts more deeply (line 129-130 and Supplementary Figure S1D).Unlike for neural avalanches, we did not find distributions according to a power law.We believe that this is because we study exclusively stimulus-evoked assemblies (see also reply to Reviewer #1 above).
-The assembly study ignores the inhibitory neuron.Why? Do they show similar behavior?

Response:
We now motivate our focus on the excitatory subpopulation only in the introduction (lines 76-77).
-Fig.7 shows that there are some areas of empty part, indicating there are other factors.What could be them?together with: -Together with the last question, I guess the dynamics is one of them or even a higher level factor than the connections that are studied by the authors.Dynamics is determined by many factors such as input (bottom up sensory inputs + top down inputs + noise), connectivity, single-neuron electrophysiology, synaptic dynamics, and E-I balance, etc.For example, below two papers contained results about how network dynamics affect assembly dynamics, form and its function.

Response:
We thank the reviewer for pointing out that we did not adequately explain this.Our structural measures indeed cannot fully explain assembly membership, as expected in a network with complex dynamics.We now explain this and outline relevant literature in lines [380][381][382][383][384][385].1 shows that a single noise source is injected to all neurons.This is problematic because it gives rise to quite some correlation between neurons.

Response:
We are not injecting the same noise into all neurons.We apologize for the lack of clarity in that regard.We have updated the paragraph (line 489) to better explain that neurons receive noise with the similar statistics, but statistically independent.